For reasons we will describe, our architecture exploits the GKP encoding.
For notational convenience we restrict our discussion to square-lattice GKP encoding but the results can be generalized to GKP states on other lattices.
In their ideal form, the GKP qubit states \(\mathinner {|{0}\rangle }_{\rm gkp}\)  and \(\mathinner {|{1}\rangle }_{\rm gkp}\)  are defined as Dirac delta combs with a spacing of \(2\sqrt{\pi }\)  in position space [1]}:
\(\mathinner {|{\mu }\rangle }_{\rm gkp} = \sum _{n} \mathinner {|{(2n+\mu )\sqrt{\pi }}\rangle }_q,\,\mu =0,1.\) 
